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Statistics Lesson 2 Normal Distribution
Name_________________________
There are many ways to examine data. One type of graphical representation is
called a density curve. The distribution of certain types of data take on the
appearance of a bell-shaped curve called a normal curve. It is the graph of a
normal distribution.
5 Characteristics of a Normal Distribution
1.
2.
3.
4.
The mean, median and mode are equal.
The graph of a normal distribution is called a normal curve.
A normal curve is bell-shaped and symmetrical about the mean.
A normal curve never touches, but gets closer and closer to the x-axis as it
gets farther from the mean.
5. The total area under the curve is equal to one.
Examples of Normally Distributed Data:
The mean and standard deviation of a normal distribution affect the location and
shape of the curve. The vertical line of symmetry of the normal distribution falls
at the mean and the width (or spread) of the curve is determined by the standard
deviation. The greater the standard deviation, the wider (flatter or less peaked)
the distribution of the data.
68-95-99.7 Rule - Empirical Rule
The mean is located on the line of symmetry of the curve.
In a normal distribution: mean = median = mode
68% of the data values fall within 1 standard deviation (  ) of the mean (  )
95% of the data values fall within 2 standard deviations of the mean
99.7% of the data values fall within 3 standard deviations of the mean
This is often referred to the 68-95-99.7 rule.
Example 1: A machine fills 12 ounce potato chip bags. It places chips in the bags. Not all bags
weigh exactly 12 ounces. The weight of the chips places is normally distributed with a mean of
12.4 ounces and with a standard deviation 0.2 ounces.
Fill in the given data on the graph.
How many standard deviations from the mean is 12 oz?____________
If you purchase a bag filled by this dispenser what is the likelihood it has less than
12 ounces?
_________%
Example 2: A normally distributed set of 240 values has a mean of 30 and a standard deviation
of 3. Approximately how many values are expected to be between 27 and 36?
Fill in the given data on the graph.
Normal Distribution & Empirical Rule Turn-In
1.
The time spent daily on Facebook by high school students is normally distributed with a
mean of 110 minutes and a standard deviation of 15 minutes. Approximately what
percentage of such users spend between 80 and 140 minutes on Facebook?
z0 
 110

15
z1 
-110

15
Fill in the data on the graph.
Approximately what % of such users spend between 80 and 140 minutes on Facebook?_______
2. The time required for women on high school track teams to run the 3200 meter race is
normally distributed with a mean of 12.4 minutes and a standard deviation of 0.7 minutes.
What percentage of women have times less than 11.7 minutes?
z
-

Fill in the data on the graph. Use Figure 1 to help answer the question above.